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Preliminary Analysis of the Target System Magnets Version with a 6-T copper magnet insert

Preliminary Analysis of the Target System Magnets Version with a 6-T copper magnet insert Version with a 6-T high-temperature superconductor insert Deformations of the WC shield due to gravity. Robert Weggel Particle Beam Lasers Nov. 30, 2010.

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Preliminary Analysis of the Target System Magnets Version with a 6-T copper magnet insert

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  1. Preliminary Analysis of the Target System Magnets • Version with a 6-T copper magnet insert • Version with a 6-T high-temperature superconductor insert • Deformations of the WC shield due to gravity. • Robert Weggel • Particle Beam Lasers • Nov. 30, 2010

  2. The IDS80d magnet configuration suffered from too high peak field in the superconducting magnets near the target, and from too high fields in these magnets if the 6-T copper magnet insert were to trip off. A revised configuration, IDS80e, mitigates these issues.

  3. IDS80d Beam is upwards Upstream solenoids of 20 T, 2.3 GJ target magnet “ids80d”. Left: Windings cross section and field magnitude (contours) & direction (arrows). Innermost three solenoids are copper hollow conductor (B = 6 T; P = 8.8 MW); others shown are Nb3Sn. Bmax = 20.08 T; B = 20 T at z = 0, −34 cm, −43 cm & −74 cm. Center: Hoop strain; εmax = 0.463% if orthotropic Young’s modulus components {Eφ, Er, Ez} = {100, 20, 20} GPa. Right: von Mises stress, σvM; max. σvM = 473 MPa.

  4. IDS80d Beam is upwards Principal stresses. Left: circumferential (hoop) stress, σφ; maximim σφ = 469 MPa. Center: radial stress, σr. Right: Axial stress, σz; max. compression = 62 MPa. Axial load on most-upstream Nb3Sn solenoid is 162 MN (downstream direction); loads, in MN, on successive solenoids = {142, −66, −71, −22, −35, −36}.

  5. IDS80d

  6. IDS80e with lower peak field in SC magnets Beam is upwards Upstream solenoids of HC&SC20T# target magnet with 6 T, 10.0 MW magnet of copper hollow conductor in 14 T SC magnet; magnetic energy = 1.18 GJ. Left: Windings cross section and field magnitude (contours) & direction (arrows); maximum BSC = 14.6 T. Center: Hoop strain with orthotropic Young’s modulus components {Eφ, Er, Ez} = {100, 20, 20} GPa; εmax = 0.326%. Right: von Mises stress, σvM; max. σvM = 340 MPa.

  7. IDS80e with lower peak field in SC magnets

  8. Replacement of the 6-T copper magnet insert by a 6-T high temperature superconducting magnet could be attractive. However, the peak stresses is the HTS coil would exceed the capability of any present conductor,  need significant conductor R&D before this option is viable.

  9. Four-Coil Magnet System near the Target Inner 2 coils are HTS, 3rd is Nb3Sn, 4th is NbTi Beam is upwards. The coils are symmetric about z = 0. Four-coil 20-T pion-capture magnet. Annular spacing = 2 cm. Inner HTS magnet: I.R. ≡ a11 = 80 cm; O.R. ≡ a21 = 98 cm; half length ≡ b1 = 120 cm; half gap ≡ g1 = 41.7 cm; coil current density ≡ j1 = 23.4 A/mm2; central field contribution ∆B1 = 2 T; maximum ambient field B1 = 21.5 T. Outer HTS coil: a22 = 118 cm; b2 = 130 cm; j2 = 23.1 A/mm2; ∆B2 = 4 T; B2 = 19.8 T. Nb3Sn coil: a23 = 148 cm; b3 = 150 cm; j3 = 19.0 A/mm2; ∆B3 = 5 T; B3 = 14.6 T. NbTi coil: a24 = b4 = 180 cm; j4 = 32.4 A/mm2; ∆B4 = 9 T; B4 = 10.8 T. Left: First-quadrant cross section, field magnitude (contours) & direction (arrows). Right: Field homogeneity is 1% over z = +/- 40 cm.

  10. Stress, Strain and Deformation in Magnets of Slide 9 Stress, strain and deformation in magnets of slide 9 with orthotropic windings. Young’s moduli {Er, Eφ, Ez} = {26, 130, 65} GPa in HTS coils and {20, 100, 40} GPa in LTS coils. 130 GPa derived from 50% Hastelloy of 220 GPa[13] + 25% copper of 80 GPa (320 MPa stress @ 0.4% strain) + 25% coolant & insulation (negligible stiffness). 100 GPa derived from 35% steel of ~230 GPa[14] + 25% Cu + 40% residual for Nb3Sn coil and, for NbTi coil, 20% steel + 40% Cu of ~135 GPa[15] + 40% residual. Left: Von Mises stress, averaged locally over winding; maximum stress in consecutive coils = {535, 549, 406, 288} MPa. Center: Hoop strain, εφ; max. percent = {0.40, 0.41, 0.38, 0.21}. Right: Deformation (magnified tenfold) ranges from 2.2 mm to 6.9 mm; contour interval = 0.25 mm.

  11. Principal Stresses in Magnets of Slide 9 Principal stresses in magnets of slide 9. Left: Hoop stress σφ; max. MPa = {515, 516, 362, 159}. Center: Radial stress σr; max. MPa = {6.5, 2.6, 1.6, −12.4}. Right: Axial stress σz; max. MPa = {-49, −65, −78, −180}.

  12. 5-Coil Design with No Miplane Gap Reversed Current in the 5th, Outer Coil 5-Coil design that eliminates midplane gap by use of reverse-current field-homogenization coil. Inner HTS coil: a11 = 80 cm; a21 = 88.7 cm; b1 = 150 cm; j1 = 25.2 A/mm2; ∆B1 = 2.4 T; B1 = 20.3 T. Outer HTS coil: a12 = 90.7 cm; a22 = 103.5 cm; b2 = 160 cm; j2 = 26.1 A/mm2; ∆B2 = 3.6 T; B2 = 17.7 T. Nb3Sn coil: a23 = 130.5 cm; b3 = 175 cm; j3 = 23.1 A/mm2; ∆B3 = 5 T; B3 = 14.1 T. NbTi coil: a24 = 153.4 cm; b4 = 200 cm; j4 = 47.2 A/mm2; ∆B4 = 10.1 T; B4 = 11.0 T. Field-homogenizing coil: a25 = 170.2 cm; b5 = 40 cm; j5 = −j4; ∆B5 = −2.09 T; B5 = 7.7 T. Left: First-quadrant cross section and field magnitude (contours) & direction (arrows). Center: Hoop strain εφ; max. percent εφ = {0.36, 0.37, 0.39, 0.37, 0.32}. Right: von Mises stress; max. MPa = {480, 496, 406, 315, 328}.

  13. Magnet volume, kiloampere-meters & magnetic energy vs. bore diameter. Reducing the magnet bore by a factor of two would decrease its kA-m by a factor of three, and its volume and energy by a factor of six.

  14. The WC shield weighs ~ 100 tons, and must be supported off the superconducting magnet cryostat. The following models are “2-D”  no stiffening due to end disks or internal ribs. The tungsten-carbide beads + water is modeled as a liquid. Even with 3-cm-thick walls, the deformations are of order 1 cm.

  15. WC Shield, supported from Top 3-cm-thick walls Approximate the WC as a liquid, so center tube “floats” upwards Deformation, magnified tenfold, of horizontal steel cylinders, fixed at 12 o’clock, with annulus of 10 g/cm3 fluid; r1 = 15 cm; dr1 = 3 mm; r2 = 72 cm; dr2= 3 cm.

  16. WC Shield, supported from Bottom 3-cm-thick walls Approximate the WC as a liquid, so center tube “floats” upwards Deformation, magnified tenfold, of horizontal steel cylinders, fixed at 6 o’clock, with annulus of 10 g/cm3 fluid; r1 = 15 cm; dr1 = 3 mm; r2 = 72 cm; dr2= 3 cm.

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